Superstatistical modelling of protein diffusion dynamics in bacteria

TL;DR

This paper introduces a superstatistical model for protein diffusion in bacteria, capturing the heterogeneity in diffusion constants and anomalous exponents, and aligns well with experimental observations of q-Gaussian displacement distributions.

Contribution

It develops a hierarchical superstatistical model incorporating joint fluctuations of diffusion parameters, advancing understanding of heterogeneous bacterial protein dynamics.

Findings

Model reproduces q-Gaussian displacement distributions.

Captures heterogeneity in diffusion constants and exponents.

Aligns closely with experimental data.

Abstract

A recent experiment [Sadoon AA, Wang Y. 2018 Phys. Rev. E 98, 042411] has revealed that nucleoid associated proteins (i.e., DNA-binding proteins) exhibit highly heterogeneous diffusion processes in bacteria where not only the diffusion constant but also the anomalous diffusion exponent fluctuates for the various proteins. The distribution of displacements of such proteins is observed to take a q-Gaussian form, which decays as a power law. Here, a statistical model is developed for the diffusive motion of the proteins within the bacterium, based on a superstatistics with two variables. This model hierarchically takes into account the joint fluctuations of both the anomalous diffusion exponents and the diffusion constants. A fractional Brownian motion is discussed as a possible local model. Good agreement with the experimental data is obtained.